# Using algebra, how do you find the smallest three consecutive integers whose sum is greater than 20?

Nov 16, 2016

Find that the three integers are: $6 , 7 , 8$

#### Explanation:

Suppose the middle consecutive integer is $n$.

Then we want:

$20 < \left(n - 1\right) + n + \left(n + 1\right) = 3 n$

Dividing both ends by $3$ we find:

$n > \frac{20}{3} = 6 \frac{2}{3}$

So the smallest integer value of $n$ which satisfies this is $n = 7$, making the three integers: $6 , 7 , 8$